Fractional Ginzburg-Landau equation for fractal media

被引：166

作者：

Tarasov, VE ^{[1
]}

Zaslavsky, GM

机构：

[1] Moscow MV Lomonosov State Univ, Skobeltsyn Inst Nucl Phys, Moscow 119992, Russia

[2] NYU, Courant Inst Math Sci, New York, NY 10012 USA

[3] NYU, Dept Phys, New York, NY 10003 USA

来源：

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2005年 / 354卷

基金：

美国国家科学基金会;

关键词：

fractional equation; fractional derivatives and integrals fractal medium; Ginzburg-Landau equation;

D O I：

10.1016/j.physa.2005.02.047

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We derive the fractional generalization of the Ginzburg-Landau equation from the variational Euler-Lagrange equation for fractal media. To describe fractal media we use the fractional integrals considered as approximations of integrals on fractals. Some simple solutions of the Ginzburg-Landau equation for fractal media are considered and different forms of the fractional Ginzburg-Landau equation or nonlinear Schrodinger equation with fractional derivatives are presented. The Agrawal variational principle and its generalization have been applied. (c) 2005 Elsevier B.V. All rights reserved.

引用

页码：249 / 261

页数：13

共 50 条

[21] Numerical solution of Ginzburg-Landau equation for superconducting networks
Kato, M
Sato, O
PHYSICA C-SUPERCONDUCTIVITY AND ITS APPLICATIONS, 2003, 392 : 396 - 400
[22] On the existence of nontrivial stable solutions to the Ginzburg-Landau equation
Jimbo, S
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 30 (02) : 811 - 817
[23] A remark on global bifurcations of solutions of Ginzburg-Landau equation
Hirano, Norimichi
Rybicki, Slawomir
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2011, 12 (06) : 2943 - 2946
[24] Complex Ginzburg-Landau Equation with Boundary Control and Observation
Li, Jing
Zhang, Zhixiong
PROCEEDINGS OF 2016 2ND INTERNATIONAL CONFERENCE ON CONTROL SCIENCE AND SYSTEMS ENGINEERING (ICCSSE), 2016, : 114 - 118
[25] ON THE CAUCHY-PROBLEM OF A GENERALIZED GINZBURG-LANDAU EQUATION
DUAN, JQ
HOLMES, P
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1994, 22 (08) : 1033 - 1040
[26] Analysis of iterative methods for solving a Ginzburg-Landau equation
Borzi, A
Grossauer, H
Scherzer, O
INTERNATIONAL JOURNAL OF COMPUTER VISION, 2005, 64 (2-3) : 203 - 219
[27] Convergence towards attractors for a degenerate Ginzburg-Landau equation
N. I. Karachalios
N. B. Zographopoulos
Zeitschrift für angewandte Mathematik und Physik ZAMP, 2005, 56 : 11 - 30
[28] Properties of the solutions of the Ginzburg-Landau equation on the bifurcation branch
Myrto Sauvageot
Nonlinear Differential Equations and Applications NoDEA, 2003, 10 : 375 - 397
[29] A finite-difference solution of the Ginzburg-Landau equation
Willers, J
Twizell, EH
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2003, 9 (12) : 1059 - 1068
[30] CHEBYSHEV WAVELET COLLOCATION METHOD FOR GINZBURG-LANDAU EQUATION
Secer, Aydin
Bakir, Yasemin
THERMAL SCIENCE, 2019, 23 : S57 - S65

← 1 2 3 4 5 →